Ok, I need to amend my previous statement with some more useful information.
I played with the video again last night and DID get auto-focus motor noise. A fair amount of it. I looked over the 2 videos and found what was the cause... the lens, shooting environment and available light.
The first video I took was outside with my dogs running around. There was plenty of background noise, barking and meet talking to mask any noise generated by the super quiet AF motor on the Tamaron 70-300 lens. What I think also helped was that it was very bright outside and the longer DOF at f13 there just wasn't as much focusing happening.
The second video was indoors with the kit 18-105mm lens. Darker so the f-values were much lower (3.5?) creating the need for more focusing and a lot quieter so the AF motor noise was more pronounced. The motor on the kit lens, in my opinion, was the biggest factor here. It's not "loud" per-se, but the built-in mic is right next to the thing so anything above a low whir is going to be picked up prominently.
Hope this helps